Interaction of dilute colloidal particles in a mixed solvent

Critical Casimir interactions between colloids around the critical point of binary solvents

Critical Casimir interactions between colloidal particles arise from the confinement of fluctuations of a near-critical solvent in the liquid gap between closely-spaced particles. So far, the comparison of theoretical predictions and experimental measurements of critical Casimir forces (CCFs) has focused on the critical solvent composition, while it has been lacking for off-critical compositions. We address this issue by investigating CCFs between spherical colloidal particles around the critical point of a binary solvent through a combination of experiments, previous Ising Monte Carlo simulation results and field-theoretical methods. By measuring the correlation length of the near-critical solvent and the pair potentials of the particles in terms of radial distribution functions and by determining the second virial coefficient, we test in detail theoretical predictions. Our results indicate that the critical Casimir theory gives quantitative correct predictions for the interaction potential between particles in a near critical binary mixture if weak preferential adsorption of the particle surface is taken into account.

Molecular dynamics simulation of a binary mixture near the lower critical point

2,6-lutidine molecules mix with water at high and low temperatures but in a wide intermediate temperature range a 2,6-lutidine/water mixture exhibits a miscibility gap. We constructed and validated an atomistic model for 2,6-lutidine and performed molecular dynamics simulations of 2,6-lutidine/water mixture at different temperatures. We determined the part of demixing curve with the lower critical point. The lower critical point extracted from our data is located close to the experimental one. The estimates for critical exponents obtained from our simulations are in a good agreement with the values corresponding to the 3D Ising universality class.

Quantification of nanoparticle interactions in pure solvents and a concentrated PDMS solution as a function of solvent quality

Using turbidity measurements, we quantified the interactions between PDMS-grafted silica nanoparticles (PDMS-g-silica) in pure solvents and a concentrated polymer solution with a focus on detecting the impact of solvent quality on graft layer stretching. This work is an extension of our previous work where we showed that interfacial wetting of the grafted polymer leads to depletion restabilization in semidilute and concentrated polymer solutions in good solvents (Dutta, N.; Green, D. Langmuir 2008, 24, 5260-5269). Subsequently, we showed that the criterion for depletion restabilization holds for both good and marginally poor solvents (Dutta, N.; Green, D. Langmuir 2010, 26, 16737-16744). In this work, we quantified nanoparticle interactions in terms of the second virial coefficient (B2), which captures the stretching of the brush in a good solvent in comparison to compression in a poor solvent. The transition from stretching to compression of the graft layer as a function of solvent quality was also supported by self-consistent mean-field (SCF) calculations. The PDMS-g-silica nanoparticles in a concentrated polymer solution in a good solvent within the complete wetting region behaved as though they were in a good solvent rather than in a polymer melt where on the basis of the SCF calculations the graft layers were expected to behave ideally. Overall, our results indicate that turbidity measurements can be used to determine the second virial coefficients for polymer-grafted nanoparticles in solvents and concentrated polymer solutions, and the relative values of the coefficients correspond well to those from theoretical calculations.

Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture

We examine the solvent-mediated interaction between two neutral colloidal particles due to preferential adsorption in a near-critical binary mixture. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. We calculate the free energy and the force between two colloidal particles as functions of the temperature T, the composition far from the colloidal particles c(∞), and the colloid separation ℓ. The interaction is much enhanced when the component favored by the colloid surfaces is poor in the reservoir. For such off-critical compositions, we find a surface of a first-order bridging transition ℓ=ℓ(cx)(T,c(∞)) in the T-c(∞)-ℓ space in a universal, scaled form, across which a discontinuous change occurs between separated and bridged states. This surface starts from the bulk coexistence surface (CX) and ends at a bridging critical line where ℓ is determined by T as ℓ=ℓ(c)(T). On approaching the critical line, the discontinuity vanishes and the derivatives of the force with respect to T and ℓ both diverge. Furthermore, bridged states continuously change into separated states if c(∞) (or T) is varied from a value on CX to a value far from CX with ℓ kept smaller than ℓ(c)(T).

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.

Critical adsorption on nonspherical colloidal particles

We consider a nonspherical colloidal particle immersed in a fluid close to its critical point. The temperature dependence of the corresponding order parameter profile is calculated explicitly. We perform a systematic expansion of the order parameter profile in powers of the local curvatures of the surface of the colloidal particle. This curvature expansion reduces to the short distance expansion of the order parameter profile in the case that the solvent is at the critical composition.

Colloidal aggregation in polymer blends

We consider here a low-density assembly of colloidal particles immersed in a critical polymer mixture of two chemically incompatible polymers. We assume that, close to the critical point of the free mixture, the colloids prefer to be surrounded by one polymer (critical adsorption). As result, one is assisted to a reversible colloidal aggregation in the nonpreferred phase, due the existence of a long-range attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gas-liquid transition. We are interested in a quantitative investigation of the phase diagram of the immersed colloids. We suppose that the positions of particles are disordered, and the disorder is quenched and follows a Gaussian distribution. To apprehend the problem, use is made of the standard phi(4) theory, where the field phi represents the composition fluctuation (order parameter), combined with the standard cumulant method. First, we derive the expression of the effective free energy of colloids and show that this is of Flory-Huggins type. Second, we find that the interaction parameter u between colloids is simply a linear combination of the isotherm compressibility and specific heat of the free mixture. Third, with the help of the derived effective free energy, we determine the complete shape of the phase diagram (binodal and spinodal) in the (Psi,u) plane, with Psi as the volume fraction of immersed colloids. The continuous "gas-liquid" transition occurs at some critical point K of coordinates (Psi(c) = 0.5,u(c) = 2). Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.

Wetting-induced effective interaction potential between spherical particles

Using a density-functional-based interface displacement model, we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one-component substance or the A-rich liquid phase of a binary liquid mixture composed of A and B particles. If this solvent is thermodynamically close to a first-order fluid-fluid phase transition, the spheres are covered with wetting films of the incipient bulk phase, i.e., the liquid phase or the B-rich liquid, respectively. Below a critical distance between the spheres their wetting films snap to a bridgelike configuration. We determine phase diagrams for this morphological transition, and analyze its repercussions on the effective interaction potential. Our results are accessible to various types of force microscopy and scattering experiments, and may be relevant to flocculation in colloidal suspensions.